Project #162539 - exercise 3

Mathematics Tutors

Subject Mathematics
Due By (Pacific Time) 01/11/2017 12:00 am

  (a) Estimate whether the following pairs of scores for x and y reflect a positive relationship, a negative relationship, or no relationship.


     x       y

   64      66

  40        79

  30        98

  71       65

  55       76

  31       83

   61     68

  42       80

  57     72


(b)  Construct a scatterplot for x and y. Verify that the scatterplot does not describe a pronounced curvilinear trend

 (c) Calculate r using the computation formula (6.1)  

Number of cards

Friends         sent                        received

Andrea           5                              10

Mike               7                              12

Doris             13                             14

Steve            9                               18

John              1                                 6


6.10  On the basis of an  extensive survey, the California Department of Education reported an r of -.32 for the relationship between TV and the achievement test scores of school children.  Each following statements represent a possible interpretation of this finding. Indicate whether each is true or false.  

(a)  Every child who watches a lot of TV will perform poorly on the achievement tests

(b) Extensive TV viewing causes a decline in test scores

(c) Children who watch little TV will tend to perform well on the tests

(d) Childeren who perfomr well on the tests will tend to watch little TV

(e) If Gretchen's TV-viewing time is reduced by one-half, we can expect a substantial improvement in her test scores

(f) TV viewing could not possibly cause a decline in test scores


6.11  Assume that an r of .80 describes the relationship between daily food intake, measured in ounces and body weight, measured in pounds, for a group of adults. Would a shift in the units of measurements from ounces to grams and from pounds to kilograms change the value of R?  Justify your answer



Chapter 7 


7.8  Each of the following pairs represents the number of licensed drivers (x) and the number of cars (y) for seven houses in my neighborhood


Drivers                         Cars

5                                  4

5                                  3

2                                  2

2                                  2

3                                  2

1                                  1

2                                 2


(a) construct a scatterplot to verify a lack of pronounced curvilinearity


(b)  determine tha least squares equation for these data. (Remember , you will first have to calculate r, ssy, and ssx)

(c) determine the standard error of estimate, S y/x given that n=7

(d)  predict the number of cars for each of two vew families with two and five drivers


7.10  Assume that R2 equals .50 for the relationship between height and weight for adults. Indicate whether the following statements are true or false


(a) fifty percent of the variablity in heights can be explained by variability  in weight

(b) there is a cause0effect relationship between height and weight

(c) the heights of 50 percent of adults can be predicted exactly from their weights

(d)  fifty percent of the variability in weights is predicted from height

7.13 In the original study of regression towards the mean, Sir Francis Galton noted a tendency for offspring of both tall and short parents to drift toward the mean height for offspring and referred to this tendency as " regression toward mediocrity". What is wrong with this conclusion that eventually all height will be close to their mean? 


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